Dimensionality Reduction Tool Research Articles

Principal Component Analysis Enhanced with Bootstrapped Confidence Interval for the Classification of Parkinsonian Patients Using Gaussian Mixture Model and Gait Initiation Parameters.

Parkinson's disease is one of the major neurodegenerative diseases that affects the postural stability of patients, especially during gait initiation. There is actually an increasing demand for the development of new non-pharmacological tools that can easily classify healthy/affected patients as well as the degree of evolution of the disease. The experimental characterization of gait initiation (GI) is usually done through the simultaneous acquisition of about 20 variables, resulting in very large datasets. Dimension reduction tools are therefore suitable, considering the complexity of the physiological processes involved. The principal Component Analysis (PCA) is very powerful at reducing the dimensionality of large datasets and emphasizing correlations between variables. In this paper, the Principal Component Analysis (PCA) was enhanced with bootstrapping and applied to the study of the GI to identify the 3 majors sets of variables influencing the postural control disability of Parkinsonian patients during GI. We show that the combination of these methods can lead to a significant improvement in the unsupervised classification of healthy/affected patients using a Gaussian mixture model, since it leads to a reduced confidence interval on the estimated parameters. The benefits of this method for the identification and study of the efficiency of potential treatments is not addressed in this paper but could be addressed in future works.

Deep learning assisted XRF spectra classification

EDXRF spectrometry is a well-established and often-used analytical technique in examining materials from which cultural heritage objects are made. The analytical results are traditionally subjected to additional multivariate analysis for archaeometry studies to reduce the initial data’s dimensionality based on informative features. Nowadays, artificial intelligence (AI) techniques are used more for this purpose. Different soft computing techniques are used to improve speed and accuracy. Choosing the most suitable AI method can increase the sustainability of the analytical process and postprocessing activities. An autoencoder neural network has been designed and used as a dimension reduction tool of initial 40×2048\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$40 \ imes 2048$$\\end{document} data collected in the raw EDXRF spectra, containing information about the selected points’ elemental composition on the canvas paintings’ surface. The autoencoder network design enables the best possible reconstruction of the original EDXRF spectrum and the most informative feature extraction, which has been used for dimension reduction. Such configuration allows for efficient classification algorithms and their performances. The autoencoder neural network approach is more sustainable, especially in processing time consumption and experts’ manual work.

Inexact augmented Lagrangian method-based full-waveform inversion with randomized singular value decomposition

Abstract The main advantage of full-waveform inversion (FWI) is the ability to obtain useful subsurface structure information, such as velocity and density, from complex seismic data. We have developed a novel inversion algorithm to improve the capability of FWI to achieve high-resolution imaging, even under complex conditions caused by random noise contamination, initial model dependence, or the selection of parameters to be estimated. Our algorithm considers an effective image processing and dimension reduction tool, randomized singular value decomposition-weighted truncated nuclear norm regularization, for embedding FWI to achieve high-resolution imaging results. This algorithm obtains a truncated matrix approximating the original matrix by reducing the rank of the velocity increment matrix, thus achieving the truncation of noisy data, with the truncation range controlled by weighted truncated nuclear norm regularization. Subsequently, we employ an inexact augmented Lagrangian method algorithm in the optimization to compress the solution space range, thus relaxing the dependence of FWI and randomized singular value decomposition-weighted truncated nuclear norm regularization on the initial model and accelerating the convergence rate of the objective function. We tested on one set of synthetic data, and the results show that, compared with traditional FWI, our method can more effectively suppress the impact of random noise, thus obtaining higher resolution and more accurate subsurface model information. This work indicates that the combination of randomized singular value decomposition-weighted truncated nuclear norm regularization and FWI is an effective imaging strategy that can help to solve the challenges faced by traditional FWI.

Robust Principal Component Analysis: A Median of Means Approach.

Principal component analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in statistics, machine learning, computer vision, and related fields. However, PCA is well-known to fall prey to outliers and often fails to detect the true underlying low-dimensional structure within the dataset. Following the Median of Means (MoM) philosophy, recent supervised learning methods have shown great success in dealing with outlying observations without much compromise to their large sample theoretical properties. This article proposes a PCA procedure based on the MoM principle. Called the MoMPCA, the proposed method is not only computationally appealing but also achieves optimal convergence rates under minimal assumptions. In particular, we explore the nonasymptotic error bounds of the obtained solution via the aid of the Rademacher complexities while granting absolutely no assumption on the outlying observations. The derived concentration results are not dependent on the dimension because the analysis is conducted in a separable Hilbert space, and the results only depend on the fourth moment of the underlying distribution in the corresponding norm. The proposal's efficacy is also thoroughly showcased through simulations and real data applications.

An Exploration of the Application of Principal Component Analysis in Big Data Processing

Abstract With the arrival of the significant data era, efficiently processing large-scale multidimensional data has become challenging. As a powerful data dimensionality reduction tool, Principal Component Analysis (PCA) plays a vital role in big data processing, especially in information extraction and data simplification, showing unique advantages. The research aims to simplify the data processing process and improve the data processing efficiency by PCA method. The research method adopts the basic theory of PCA, the improvement of the weighted principal component analysis algorithm, and standardized and homogenized data processing techniques to process large-scale multidimensional data sets. The results show that the data dimensionality is significantly reduced after using PCA, for example, in the Analysis of the earnings quality of listed companies in the e-commerce industry, the cumulative variance contribution rate of the first four principal components extracted by PCA reaches 81.623%, which effectively removes the primary information of the original data. PCA not only reduces the complexity of the data, but also retains a large amount of crucial information, which is a significant application value for the processing of big data, especially in the fields of data compression and pattern recognition.

Varying Coefficient Model via Adaptive Spline Fitting

The varying coefficient model is a potent dimension reduction tool for nonparametric modeling and has received extensive attention from researchers. Most existing methods for fitting this model use polynomial splines with equidistant knots and treat the number of knots as a hyperparameter. However, imposing equidistant knots tends to be overly rigid, and systematically determining the optimal number of knots is also challenging. In this article, we address these challenges by employing polynomial splines with adaptively selected and predictor-specific knots to fit the varying coefficients in the model. We propose an efficient dynamic programming algorithm to find the optimal solution. Numerical results demonstrate that our new method achieves significantly smaller mean squared errors for coefficient estimations compared to the equidistant spline fitting method. An implementation of our method in R is available at https://github.com/wangxf0106/vcmasf. Proofs of the theorems are provided in the online supplementary materials.

Guided optimization of ToxPi model weights using a Semi-Automated approach

The Toxicological Prioritization Index (ToxPi) is a visual analysis and decision support tool for dimension reduction and visualization of high throughput, multi-dimensional feature data. ToxPi was originally developed for assessing the relative toxicity of multiple chemicals or stressors by synthesizing complex toxicological data to provide a single comprehensive view of the potential health effects. It continues to be used for profiling chemicals and has since been applied to other types of “sample” entities, including geospatial (e.g. county-level Covid-19 risk and sites of historical PFAS exposure) and other profiling applications. For any set of features (data collected on a set of sample entities), ToxPi integrates the data into a set of weighted slices that provide a visual profile and a score metric for comparison. This scoring system is highly dependent on user-provided feature weights, yet users often lack knowledge of how to define these feature weights. Common methods for predicting feature weights are generally unusable due to inappropriate statistical assumptions and lack of global distributional expectation. However, users often have an inherent understanding of expected results for a small subset of samples. For example, in chemical toxicity, prior knowledge can often place subsets of chemicals into categories of low, moderate or high toxicity (reference chemicals). Ordinal regression can be used to predict weights based on these response levels that are applicable to the entire feature set, analogous to using positive and negative controls to contextualize an empirical distribution. We propose a semi-supervised method utilizing ordinal regression to predict a set of feature weights that produces the best fit for the known response (“reference”) data and subsequently fine-tunes the weights via a customized genetic algorithm. We conduct a simulation study to show when this method can improve the results of ordinal regression, allowing for accurate feature weight prediction and sample ranking in scenarios with minimal response data. To ground-truth the guided weight optimization, we test this method on published data to build a ToxPi model for comparison against expert-knowledge-driven weight assignments.

BinaryClust2: An Integrated Computational Pipeline for Systematic Mining of Mass Cytometry Data to Assist Deep Immune Profiling in Haematological Research

Introduction: The key role of immune system in modulating treatment efficacy and clinical outcomes in the settings of haematological diseases has been well recognized through the application of flow cytometry technologies over years. Mass cytometry (MC) is a next generation cytometry platform to simultaneously profile over 40 protein markers on single-cell resolution, which facilitates clinical research on immune monitoring and biomarker discovery. Nonetheless, the high-dimensional data generated present a daunting challenge for clinical investigators. Therefore, we describe BinaryClust2 (https://github.com/JingAnyaSun/BinaryClust2), an R-based computational framework integrated with the state-of-the-art algorithms and novel cell lineage characterisation method to assist comprehensive exploration of liquid MC data. Method: Here, we present the implementation of BinaryClust2 to three example MC datasets: In-house dataset from peripheral blood mononuclear cells (PBMCs) of 9 baseline myeloproliferative neoplasm (MPN) patients (~4 million cells), previously published data from 11 MPN patients receiving influenza vaccine (~0.2million cells), and published dataset of 59 covid patients and 23 healthy donors (~2million cells). BinaryClust2 has a streamlined analytical workflow, which comprises the following steps (Figure 1A): Step 1: Quality control, batch effect evaluation and correction Data quality control is a separate step before downstream analysis which includes diagnostic plots and batch effect examination. Algorithms CytofRUV and CytoNorm are available in the pipeline to remove unwanted variations caused by batch effects. Step 2: Semi-supervised identification of main cell types BinaryClust2 adopts a knowledge-based semi-supervised approach to predict main cell types. Users are required to provide a simple marker expression matrix of pre-defined cell types along with fcs files and metadata to construct a SingleCellExperiment (SCE) object, then the embedded algorithm can automatically classify cell populations without manual annotation. Step 3: In-depth interrogation and differential testing Specific population can be further extracted from whole cells and subject to in-depth exploration using unsupervised algorithms for subpopulation discovery. Dimensionality reduction tools UMAP and TSNE, unsupervised clustering methods Phenograph and flowSOM, and various data visualization plotting functions are offered in BinaryClust2. For statistical analysis, multiple study group comparison (n>2) of cell abundance and functional marker expression is supported via Kruskal Wallis test with multiple testing correction and post hoc analysis. Results: The performance of the semi-supervised classification function was tested independently in the MPN and influenza PBMC datasets, 7 main cell lineages were identified with accuracy comparable to manual gating by human experts (Figure 1B): average F-measure reached 0.93 and 0.98 respectively. Moreover, taking manual gating as ground truth reference, BinaryClust2 outperformed the unsupervised approach flowSOM concerning accuracy (F-measure: 0.93 vs. 0.70) and speed (140s vs 339s) in MPN dataset, while remaining equivalent to the well-performing semi-supervised approach LDA in accuracy (F-measure: 0.93 vs. 0.93) but faster in runtime (140s vs 595s), as shown in Table 1. Application to covid-19 dataset by Chevrier et al. achieved reproducible results and additional discoveries. 13 main cell types were characterised, abundance of B cells, Basophils, cDCs, DN T cells, Monocytes, Neutrophils, NK cells, pDCs, CD8 T cells obtained statistical significance (all P<0.05) among study conditions (healthy, mild covid, severe covid). We also grouped markers reflecting functional status of immune cells and found Granzyme B expression was significantly increased in the majority of main immune cells of covid patients. Phenograph was further applied in neutrophils and monocytes and returned 14 and 16 subsets respectively. Conclusion: Overall, BinaryClust2 incorporates expert's prior biological knowledge in a semi-supervised fashion to accurately deconvolute well-defined main cell lineages, while also preserving the potential of unsupervised approaches to discover novel cell subsets and providing a user-friendly toolset to remove the analytical barrier for high-dimensional immune profiling.

Similarity-assisted variational autoencoder for nonlinear dimension reduction with application to single-cell RNA sequencing data

BackgroundDeep generative models naturally become nonlinear dimension reduction tools to visualize large-scale datasets such as single-cell RNA sequencing datasets for revealing latent grouping patterns or identifying outliers. The variational autoencoder (VAE) is a popular deep generative method equipped with encoder/decoder structures. The encoder and decoder are useful when a new sample is mapped to the latent space and a data point is generated from a point in a latent space. However, the VAE tends not to show grouping pattern clearly without additional annotation information. On the other hand, similarity-based dimension reduction methods such as t-SNE or UMAP present clear grouping patterns even though these methods do not have encoder/decoder structures.ResultsTo bridge this gap, we propose a new approach that adopts similarity information in the VAE framework. In addition, for biological applications, we extend our approach to a conditional VAE to account for covariate effects in the dimension reduction step. In the simulation study and real single-cell RNA sequencing data analyses, our method shows great performance compared to existing state-of-the-art methods by producing clear grouping structures using an inferred encoder and decoder. Our method also successfully adjusts for covariate effects, resulting in more useful dimension reduction.ConclusionsOur method is able to produce clearer grouping patterns than those of other regularized VAE methods by utilizing similarity information encoded in the data via the highly celebrated UMAP loss function.

Neonatal Hypoxic-Ischemic Encephalopathy Grading from Multi-Channel EEG Time-Series Data Using a Fully Convolutional Neural Network

A deep learning classifier is proposed for grading hypoxic-ischemic encephalopathy (HIE) in neonates. Rather than using handcrafted features, this architecture can be fed with raw EEG. Fully convolutional layers were adopted both in the feature extraction and classification blocks, which makes this architecture simpler, and deeper, but with fewer parameters. Here, two large (335 h and 338 h, respectively) multi-center neonatal continuous EEG datasets were used for training and testing. The model was trained based on weak labels and channel independence. A majority vote method was used for the post-processing of the classifier results (across time and channels) to increase the robustness of the prediction. A dimension reduction tool, UMAP, was used to visualize the model classification effect. The proposed system achieved an accuracy of 86.09% (95% confidence interval: 82.41–89.78%), an MCC of 0.7691, and an AUC of 86.23% on the large unseen test set. Two convolutional neural network architectures which utilized time-frequency distribution features were selected as the baseline as they had been developed or tested on the same datasets. A relative improvement of 23.65% in test accuracy was obtained as compared with the best baseline. In addition, if only one channel was available, the test accuracy was only reduced by 2.63–5.91% compared with making decisions based on the eight channels.

Nonlinear dimensionality reduction methods for potentiometric multisensor systems data analysis

AbstractElectrochemical multisensor systems were proven to be a very perspective research direction in modern analytical chemistry. The multisensor approach assumes an employment of cross‐sensitive chemical sensors in combination with multivariate data processing methods. Dimensionality reduction of the data obtained from multisensor systems is a very important step and it is mostly based on the traditional tools of chemometrics, such as Principal Component Analysis (PCA). In case of chemically complex samples, the response of multisensor systems may have a complex nonlinear nature and the use of linear modelling methods does not seem optimal. However, the potential of nonlinear dimensionality reduction methods in the processing of multisensor data has not yet been systematically studied. In this report we aim to fill this gap and assess the performance of various nonlinear dimensionality reduction tools: Isomap, Self‐Organizing Kohonen Maps, and Autoencoder. These methods were explored using three datasets from potentiometric multisensor systems obtained in various real applications. It was shown that nonlinear dimensionality reduction methods give the possibility to obtain additional and more detailed information about the analyzed objects/processes compared to PCA. However, calculation time for nonlinear dimensionality reduction methods essentially exceeds that for PCA, and it can be a limiting factor for application of such algorithms.

Public Usage of E-Government in EU Countries: Are There Any Consequences for Tax Evasion?

Due to the processes of digitalization and automation, the e-Government has become an essential tool of public administration. The paper deals with the problem of e-Government usage by the public and its potential connection to tax evasion. The analysis is based on available secondary panel and cross-sectional data on the level of EU countries in the period 2008 to 2021. We compare the situation in the countries and classify them into homogenous clusters based on the overall public usage of e-Government. Principal component analysis and cluster analysis have been used as tools for dimension reduction and clustering. Moreover, we also found evidence of a potential relationship between the usage of e-Government and tax evasion. The provision of online information and services by the government to its citizens as well as online communication with public authorities are related to the lower level of tax evasion in the country. Hence, public authorities should support e-Government usage and e-filing systems to fight against tax evasion.

Analyzing Nexus between Economic Complexity, Renewable Energy, and Environmental Quality in Japan: A New Evidence from QARDL Approach

The economic complexity index is an effective dimensionality reduction tool that is applied to forecast and predict future economic growth, income, and environmental quality. Renewable energy plays an important role in mitigation of carbon dioxide emissions. This study explores the nexus between economic complexity, renewable energy, FDI, trade, and environmental quality in Japan for the period 1970Q1-2019Q4. We use carbon dioxide (CO2) emissions as dependent variable while economic complexity index (ECI), foreign direct investment (FDI) inflow, renewable energy (RNE), and trade as explanatory variables. This study applies a quantile autoaggressive approach for analysis; the result of this study suggests a long-run implication of the ECI, FDI, GDP, RNE, and trade for the CO2 emissions. While only RNE and trade show mixed results in the short run, the rest of the variables do not have short-run implications. This implies that emissions mostly result in the industrial production activities only in the long run and in some quantiles only in the short run. The Japanese government may adopt different measures to reduce the CO2 emissions in the country, such as carbon tax and tax exemption on renewable energy investment. Furthermore, the government may adopt the renewal energy in production, which could achieve sustainable development goal.

Convergence of mechanistic modeling and artificial intelligence in hydrologic science and engineering

Hydrology is a mature physical science based on application of first principles. However, the water system is complex and its study requires analysis of increasingly large data available from conventional and novel remote sensing and IoT sensor technologies. New data-driven approaches like Artificial Intelligence (AI) and Machine Learning (ML) are attracting much “hype” despite their apparent limitations (transparency, interpretability, ethics). Some AI/ML applications lack in addressing explicitly important hydrological questions, focusing mainly on “black-box” prediction without providing mechanistic insights. We present a typology of four main types of hydrological problems based on their dominant space and time scales, review their current tools and challenges, and identify important opportunities for AI/ML in hydrology around three main topics: data management, insights and knowledge extraction, and modelling structure. Instead of just for prediction, we propose that AI/ML can be a powerful inductive and exploratory dimension-reduction tool within the rich hydrological toolchest to support the development of new theories that address standing gaps in changing hydrological systems. AI/ML can incorporate other forms of structured and non-structured data and traditional knowledge typically not considered in process-based models. This can help us further advance process-based understanding, forecasting and management of hydrological systems, particularly at larger integrated system scales with big models. We call for reimagining the original definition of AI in hydrology to incorporate not only today’s main focus on learning, but on decision analytics and action rules, and on development of autonomous machines in a continuous cycle of learning and refinement in the context of strong ethical, legal, social, and economic constrains. For this, transdisciplinary communities of knowledge and practice will need to be forged with strong investment from the public sector and private engagement to protect water as a common good under accelerated demand and environmental change.

Supervised kernel principal component analysis for forecasting

Principal component analysis (PCA) is a versatile tool for dimension reduction with many applications in finance, economics, and machine learning. This paper proposes a new approach to improving the forecasting ability of the Principal Components (PCs) of observed high-dimensional predictors in a factor-augmented forecasting framework. The approach is carried out in a three-step procedure, where we first perform a nonparametric kernel regression of the target variable on each predictor to obtain a new high-dimensional predictor vector formed by stacking all estimated kernel regression functions, we then extract PCs from these new predictors using PCA, and finally, we employ the extracted PCs as predictors to forecast the target variable. A real example on macroeconomic forecasting is analyzed and numerical results show that the proposed kernel PCA can outperform some commonly used forecasting approaches in out-of-sample prediction.

Deep learning pipeline for quality filtering of MRSI spectra.

With the rise of novel 3D magnetic resonance spectroscopy imaging (MRSI) acquisition protocols in clinical practice, which are capable of capturing a large number of spectra from a subject's brain, there is a need for an automated preprocessing pipeline that filters out bad-quality spectra and identifies contaminated but salvageable spectra prior to the metabolite quantification step. This work introduces such a pipeline based on an ensemble of deep-learning classifiers. The dataset consists of 36,338 spectra from one healthy subject and five brain tumor patients, acquired with an EPSI variant, which implemented a novel type of spectral editing named SLOtboom-Weng (SLOW) editing on a 7T MR scanner. The spectra were labeled manually by an expert into four classes of spectral quality as follows: (i) noise, (ii) spectra greatly influenced by lipid-related artifacts (deemed not to contain clinical information), (iii) spectra containing metabolic information slightly contaminated by lipid signals, and (iv) good-quality spectra. The AI model consists of three pairs of networks, each comprising a convolutional autoencoder and a multilayer perceptron network. In the classification step, the encoding half of the autoencoder is kept as a dimensionality reduction tool, while the fully connected layers are added to its output. Each of the three pairs of networks is trained on different representations of spectra (real, imaginary, or both), aiming at robust decision-making. The final class is assigned via a majority voting scheme. The F1 scores obtained on the test dataset for the four previously defined classes are 0.96, 0.93, 0.82, and 0.90, respectively. The arguably lower value of 0.82 was reached for the least represented class of spectra mildly influenced by lipids. Not only does the proposed model minimise the required user interaction, but it also greatly reduces the computation time at the metabolite quantification step (by selecting a subset of spectra worth quantifying) and enforces the display of only clinically relevant information.

Principal weighted least square support vector machine: An online dimension-reduction tool for binary classification

As relevant technologies advance, streamed data are frequently encountered in various applications, and the need for scalable algorithms becomes urgent. In this article, we propose the principal weighted least square support vector machine (PWLSSVM) as a novel tool for SDR in binary classification where most SDR methods suffer since they assume continuous Y. We further show that the PWLSSVM can be employed for the online SDR for the streamed data. Namely, the PWLSSVM estimator can be directly updated from the new data without having old data. We explore the asymptotic properties of the PWLSSVM estimator and demonstrate its promising performance in terms of both estimation accuracy and computational efficiency for both simulated and real data.

EMBED: Essential MicroBiomE Dynamics, a dimensionality reduction approach for longitudinal microbiome studies

Dimensionality reduction offers unique insights into high-dimensional microbiome dynamics by leveraging collective abundance fluctuations of multiple bacteria driven by similar ecological perturbations. However, methods providing lower-dimensional representations of microbiome dynamics both at the community and individual taxa levels are not currently available. To that end, we present EMBED: Essential MicroBiomE Dynamics, a probabilistic nonlinear tensor factorization approach. Like normal mode analysis in structural biophysics, EMBED infers ecological normal modes (ECNs), which represent the unique orthogonal modes capturing the collective behavior of microbial communities. Using multiple real and synthetic datasets, we show that a very small number of ECNs can accurately approximate microbiome dynamics. Inferred ECNs reflect specific ecological behaviors, providing natural templates along which the dynamics of individual bacteria may be partitioned. Moreover, the multi-subject treatment in EMBED systematically identifies subject-specific and universal abundance dynamics that are not detected by traditional approaches. Collectively, these results highlight the utility of EMBED as a versatile dimensionality reduction tool for studies of microbiome dynamics.

Partial sufficient variable screening with categorical controls

Variable screening as a fast and effective dimension reduction tool plays an important role in analyzing ultrahigh dimensional data. While a very large number of actual datasets contain both continuous and categorical variables, existing methods are mostly designed for continuous data. Partial sufficient variable screening, which aims to reduce the predictive set of primary interest without loss of regression information in the presence of some control variables, is proposed with theoretical guarantees. Specifically, for regression analyses involving mixed types of predictors, variable screening is approached under the notion of sufficiency by constraining the reduction of the continuous variables through the subpopulations identified by the categorical variables. The effectiveness of the proposed method is demonstrated through simulation studies encompassing a variety of regression and classification models, and an application in prognostic gene screening for diffuse large-B-cell lymphoma.

FISHFactor: a probabilistic factor model for spatial transcriptomics data with subcellular resolution.

Factor analysis is a widely used tool for unsupervised dimensionality reduction of high-throughput datasets in molecular biology, with recently proposed extensions designed specifically for spatial transcriptomics data. However, these methods expect (count) matrices as data input and are therefore not directly applicable to single molecule resolution data, which are in the form of coordinate lists annotated with genes and provide insight into subcellular spatial expression patterns. To address this, we here propose FISHFactor, a probabilistic factor model that combines the benefits of spatial, non-negative factor analysis with a Poisson point process likelihood to explicitly model and account for the nature of single molecule resolution data. In addition, FISHFactor shares information across a potentially large number of cells in a common weight matrix, allowing consistent interpretation of factors across cells and yielding improved latent variable estimates. We compare FISHFactor to existing methods that rely on aggregating information through spatial binning and cannot combine information from multiple cells and show that our method leads to more accurate results on simulated data. We show that our method is scalable and can be readily applied to large datasets. Finally, we demonstrate on a real dataset that FISHFactor is able to identify major subcellular expression patterns and spatial gene clusters in a data-driven manner. The model implementation, data simulation and experiment scripts are available under https://www.github.com/bioFAM/FISHFactor.